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Omnitetrachordal MOS scale
7L+5s
12 tones (5+2+5)

MOS of the meantone and flattone temperaments (slightly flat 3/2). Imperfect, but very usable at any L/s ratio. Many modes may be pentachordally split in two ways.

P = 0.7936402416
Q = 6.0713810872 (4/3 = 3L+1.5s)

L = 100.00 to 171.43 cents (153.38 cents @ Q)
s = 0.00 to 100.00 cents (25.26 cents @ Q)

9/8 = L+s (171.43 to 200.00 cents)
4/3 = 3L+2s (500.00 to 514.29 cents)
generator = 4/3

notable EDOs: 19, 26, 31, 33, 43, 45, 50, etc.

all modes:

sLLsL sL sLLsL


LLsLs Ls LLsLs

Ls LsLsL LsLsL
LsLsL sL LsLsL

sL sLsLL sLsLL


Ls LsLLs LsLLs

LsLsL LsLsL Ls
sL sLLsL sLLsL

sLsLL sLsLL sL
Ls LLsLs LLsLs

LsLLs LsLLs Ls
sL LsLsL LsLsL

sLLsL sLLsL sL


LLsLs LLsLs Ls

LsLsL Ls LsLsL
LsLsL LsLsL sL

sLsLL sL sLsLL


LsLLs Ls LsLLs


12_07_05_LsLLs_Ls_LsLLs.png

See also


References

  • Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages 3685 and 10987.